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Generalizations of the neumann system—a curve theoretical approach part III: Order n systems
Author(s) -
Schilling Randolph James
Publication year - 1992
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160450702
Subject(s) - isospectral , mathematics , integrable system , lax pair , hamiltonian system , trace (psycholinguistics) , pure mathematics , von neumann architecture , hamiltonian (control theory) , mathematical analysis , algebra over a field , mathematical physics , linguistics , philosophy , mathematical optimization
The Neumann system is a well‐known algebraically completely integrable Hamiltonian system. Its geometry has roots in hyperelliptic curve theory and the isospectral deformation theory of Hill's operator. In this paper generalizations of the Neumann system are found for n ‐sheeted Riemann surfaces and the isospectral deformation theory of operators of order n . Trace formulas, Lax pairs, and constants of motion are found. The new systems are shown to be algebraically completely integrable.